How do prophecies in the Bible show that they were written after the fact?
Are they shown to be written after the fact because they are spot on in what they claim?
They would not be written after the fact if they were mistaken in what they said.
I gave you two examples of terribly failed prophecies. So they are clearly not all "spot on". Why don't you do a little homework?
Let's take Daniel as an example.
"Dating[
edit]
The prophecies of Daniel are accurate down to the career of
Antiochus IV Epiphanes, king of Syria and oppressor of the Jews, but not in its prediction of his death: the author seems to know about Antiochus' two campaigns in Egypt (169 and 167 BC), the desecration of the Temple (the "abomination of desolation"), and the fortification of the Akra (a fortress built inside Jerusalem), but he seems to know nothing about the reconstruction of the Temple or about the actual circumstances of Antiochus' death in late 164 BC. Chapters 10–12 must therefore have been written between 167 and 164 BC. There is no evidence of a significant time lapse between those chapters and chapters 8 and 9, and chapter 7 may have been written just a few months earlier again.
[49]
Further evidence of the book's date is in the fact that Daniel is excluded from the Hebrew Bible's
canon of the prophets, which was closed around 200 BC, and the Wisdom of
Sirach, a work dating from around 180 BC, draws on almost every book of the Old Testament except Daniel, leading scholars to suppose that its author was unaware of it. Daniel is, however, quoted in a section of the
Sibylline Oracles commonly dated to the middle of the 2nd century BC, and was popular at Qumran at much the same time, suggesting that it was known from the middle of that century.
[50]"
en.wikipedia.org
Please note, the Jews themselves knew it was no a book of prophecy. The "canon of the prophets" was closed around 200 BCE and Daniel was not in it. It was as the article shows written after that date. The Jews would have known when it was written.